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The gas mileage for Peter’s car is $21$ miles per gallon when the car travels at an average speed of $50$ miles per hour. The car's gas tank has $17$ gallons of gas at the beginning of a trip. If Peter’s car travels at an average speed of $50$ miles per hour, which of the following functions $f$ models the number of gallons of gas remaining in the tank $t$ hours after the trip begins?
$A)f(t) = 17 - \dfrac{{21}}{{50t}}$
$B)f(t) = 17 - \dfrac{{50}}{{21t}}$
$C)f(t) = \dfrac{{17 - 21t}}{{50}}$
$D)f(t) = \dfrac{{17 - 50t}}{{21}}$

Last updated date: 13th Jul 2024
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Hint: First we have to define what the terms we need to solve the problem are.
As per the given problem we need to find gallons of gas after the trip.
Since we first analyzed what the given terms are as follows; the gas mileage is twenty-one per gallon and with respect to Peter's car; also, the average speed is fifty miles per hour.
Finally, the car gas tank has seventeen gallons of gas at the beginning.
Complete step by step answer:
Since Peter’s car travels at the average speed of fifty miles per hour, we just need to find the model numbers as per the gallons of gas which remains t hours after the trip;
Now we simply solve this problem by checking the number of options which means first take the option A as follows; $A)f(t) = 17 - \dfrac{{21}}{{50t}}$ since t is the trip begins after \[t\] hours but as per given the average speed if \[50\] miles per hour so there is no possible of t to be the multiply of fifty and hence it is wrong
Let us now take the option C and D which are $C)f(t) = \dfrac{{17 - 21t}}{{50}}$,$D)f(t) = \dfrac{{17 - 50t}}{{21}}$
Since as we see the options contains the seventeen minus of the \[t\]-hours in numerator
But the car gas tank has seventeen gallons and we need average and hence it will need to minus on overall not only to the numerator terms; hence options C and D are wrong
Therefore the only option left and it is also the correct option which is $B)f(t) = 17 - \dfrac{{50}}{{21t}}$ as we see correctly t-hours is times (multiplied by 21) and seventeen overall minus the average and \[t\]-hours

So, the correct answer is “Option B”.

Note: There is no general formula like we apply and get the exact answer for this types of question hence we need to eliminate other options to find the correct answer as per above solution;
$f(t)$ may be a conversion of the polynomial factors.